1. Field of the Invention
The present invention generally relates to computer systems for scheduling the generating units of electric utilities and, more particularly, to a computer implemented process which, given (1) a set of load forecasts on the electric system, (2) a prediction of trading transactions that may take place within the next few days, (3) a description of the physical properties of the generating units, (4) an estimate of spot prices, and (5) fuel prices associated with load forecasts, provides generation levels, fuel usage and prices at which power can be traded.
2. Background Description
Electricity is an essential part of our lives. If we took a moment to think of the services that would not exist if electricity were not here, we would be amazed. Almost every aspect of our modern lives involves electric power; from light bulbs and television sets to hospitals and auto industries. Although we are used to having power whenever we need it, the processes and systems involved in delivering electricity require careful planning and sophisticated mathematical and forecasting models.
Lately, due to rising costs of energy and discrepancies in its price among different regions of the country, the legal framework surrounding the electric-power industry has changed. This change has opened the door for utilities to compete with each other and against independent suppliers regardless of their geographic location. Although this change will benefit the consumer, utilities are going to face a highly unpredictable market and will need to make tough decisions regarding power generation and delivery.
Depending on the fuel used, electric-power generators of a utility may be categorized into thermal, nuclear, and hydroelectric. In general, a thermal unit uses a boiler that generates steam to drive a turbine. The turbine motion is then utilized to generate electric power. After cooling down, condensed steam (water) is pumped back into the boiler so that it can be heated again. Part of the power generated is used to drive a cooling fan and to run the system's pump. Both coal and oil can be used to fuel the boiler. To start a thermal generator quickly, natural gas is often used; then the system switches to the standard fuel. Note that the operations of a thermal unit are similar to those of a locomotive. The output of a thermal unit is a function of the heat generated in the boiler. Given that there is a limit to the amount of fuel that can be burnt during one hour, a thermal generator has a maximum generation capacity, G. Generating enough steam to drive the turbine requires a minimal amount of fuel which depends on the generating-unit's physical properties. Hence, we expect the minimum output of a generator, g, to be significantly greater than zero. To start a generator, the boiler must first be heated to the level at which it starts producing steam. The cost of the fuel used in heating the boiler is called the "start-up" cost. Note that this cost is not associated with any electric-power output.
FIGS. 1A and 1B present the relationship between the heat input to a generator and its electric-power output. The heat input is measured in British Thermal Units or BTU. The curve in FIG. 1A representing the electric-power output (MWH) is usually a second-degree polynomial in heat input. As expected, this function is increasing; i.e., as we burn more fuel we expect to generate more electricity. One can use the curve in FIG. 1A to compute the average heat input per MWH or the "unit heat-rate curve". Note that the unit heat-rate curve shown in FIG. 1B starts at a maximum rate (BTU/MWH) and declines as the load increases. This reflects the fact that the unit's efficiency increases as we increase the load towards the middle of the operating range. The efficiency usually declines after a certain load, x. To translate the curves of FIGS. 1A and 1B into a relationship between the load on a generator and the cost, one can multiply the cost per BTU ($/BTU) by the functions of FIGS. 1A and 1B.
The other classes of generators, nuclear and hydroelectric, use similar concepts to generate electricity. In the case of nuclear units, a radioactive material is used to run the reactor; while in the case of hydroelectric units, a water stream is used to push the turbines. Note that thermal and nuclear units require a lead-time (two hours or more) to start generating power. Given that there might be an urgent need for power, utilities maintain quick-start generators for unusual circumstances. These units use natural gas to heat air, not water, which is then used to push a small turbine. Clearly, these units have a smaller generating capacity than thermal units and are not as efficient. However, they have a very short start-up time (ten minutes or less) because the energy required to heat air is less than that needed to heat water. The quick-start generators are similar in their operations to jet engines.
In terms of operations, generators can be classified into three categories: "must-run units", "cyclers", and "peakers". Must-run units need to be running all the time. There is a number of reasons for this. One example is that of nuclear units. The time and energy required to start them are costly which makes switching them on and off economically infeasible. Another example is when a utility goes into a contractual agreement with a generating plant which results in continual running for a certain period.
The second category of generators is cyclers. These are units that are switched on and off depending on need. To avoid damaging these units, once a unit has been switched on, it must remain running for a minimal time duration (four to forty-eight hours). A similar constraint holds when a generator is switched off; it has to be given enough time to cool down (four to forty-eight hours). In general, starting up a cycler may take two to twenty-four hours depending on the unit. If power is needed urgently, a utility uses peaking units. These are the quick-start units mentioned above. They are costly but necessary to maintain a reliable system that can deliver power under any circumstances.
The generated electric-power is carried across transmission lines to the different points of usage or delivery points. Examples of delivery points are a city or a large factory. Whenever electric power is transmitted, part of it is lost. To maintain a reliable service, a utility must generate, at any moment, enough electricity to meet the demand of its customers plus losses incurred in power transmission. Note that exceeding customers' need increases the cost of operating the system and may cause power outages due to overloading some power lines. Given that power usage at any delivery point fluctuates continually, the problem of controlling the load on each generator while meeting the demand requires sophisticated tools.
To increase the reliability of an electric-power system, transmission lines of different utilities are connected with each other at certain points. These connections allow one utility to borrow power from another utility if needed. For example, a generator may fail suddenly resulting in shortage of generation. Being connected to neighboring utilities, the burden of generation loss is shared with others. Of course, the utility that suffered a generator loss must start another unit as quickly as possible or take action to compensate for this loss.
To meet customers' demand, a planner predicts the electric load on the system for the following week. The forecast is given in the form of total load per hour. That is, it gives the expected load at each hour for the next 168 hours. Electric utilities apply advanced statistical models to the weather forecast for each region they serve, load data from previous years, and load data from last week; and use intuition to produce an accurate forecast. Using the load forecast, a utility schedules its generating units for the next 168 hours. By scheduling, what is meant is deciding when each generator should be on or off during the week. The schedule also indicates the load on each generator in the system at each hour. To minimize the cost of operating the system, a utility attempts to find a schedule that meets the load at a minimal cost. It is important to note that the resulting schedule must take into consideration all constraints imposed by the system, such as minimum up-time and minimum down-time, which makes the scheduling task notoriously hard. The problem of finding a minimal cost schedule for the generating units is known as the "unit commitment problem".
To maintain high reliability in the electric system, a utility refines its load forecast every eight hours and solves, using the updated forecast, a new unit commitment to adjust the schedule. The new schedule must respect all constraints imposed by the previous one. For example, if a unit, that has a minimum up-time of eight hours, was switched on two hours before revising the schedule, the revision must make sure that this unit runs for at least another six hours even though this unit may not be needed. Clearly, such inefficiencies may arise if the load forecast changes significantly due to unexpected elements such as a sudden change in weather patterns or generator failure.
For a more detailed discussion on the subject of power generation and transmission, see A. J. Wood and B. E. Wollenberg, Power Generation, Operation, and Control, John Wiley, 1996.
The power industry is now going through deregulation. The current picture of a single utility controlling the market in a specific region will soon disappear. Instead, there will be power producers who sell their production to a power pool; and power suppliers who will buy power from the pool and sell it to their customers. Although the full picture of the power industry after deregulation is not yet known, it is clear that utilities need to prepare themselves for an open market in which buying and selling power are to be considered when the schedule of the generating units is created.
The main reason behind deregulation is the high price of electric energy. The first step towards deregulation was taken in 1978 with the passage of the Public Utilities Regulatory Policy Act. This act encouraged non-utility generation and required utilities to buy power from independent generators. The Energy Policy Act of 1992 took deregulation a step further by mandating open access on the transmission system for wholesales.
Currently, electricity is sold as a service that is delivered at specified points. For example, each one of us expects to receive electric power through a meter outside the house. We also pay for this service regardless of its producer or which power lines it followed. That is, the electricity bill indicates the total usage of electricity in KWH and the service price per KWH without incorporating any other details into the pricing scheme. Deregulation is changing this picture by un-bundling the electric power into generation and transmission. One will pay a production cost and a transmission fee. There will be several power suppliers from whom electric power may be purchased. Suppliers may have different pricing mechanisms. For example, there might be a discount for using power off-peak periods or for signing a long-term contract with the supplier. Power producers will compete with each other to minimize their costs so that they can sell their product to more customers and maximize their profit.
On the other hand, power transmission will remain regulated for the time being. The reason for that is to maintain a reliable system. The transmission lines in each state or region will be controlled by an independent entity called Independent System Operator or ISO. One of the ISO responsibilities is to settle financially with the parties involved in transmitting electric power. The transmission cost depends on the proximity of the supplier and the congestion of the transmission lines as well as other operational factors. To maintain a reliable system, ISO announces, 24 hours in advance, the load forecast on the system and asks interested suppliers to submit bids. The ISO then holds an auction to determine which suppliers to buy power from. Note that suppliers who submit a bid with a high price may end up not selling any of their production. On the other hand, selling power at a low price may not create enough revenue for a generator. Given that no one knows in advance the amount of power that competitors may bid for, the electric-power market will become more uncertain and risky.
The hope is that deregulation will result in cheaper prices and improve the overall economy by encouraging investments in electric utilities. The size of the electric industry is expected to grow after deregulation as was the case with the telecommunications industry. In the case of telecommunications, industry revenue shot up from $81 billion to $170 billion in ten years.
On the other end of the spectrum, due to deregulation, the load on a utility system is becoming increasingly unpredictable. The reason is trading transactions that change the load pattern significantly. Some utilities, for example, may sell more than 30% of their power generation to other utilities on certain days. Demand and supply in the market are functions of volatile electricity prices which in turn depend on highly unpredictable elements such as weather conditions around the country and fuel prices which may vary within a wide range.